Geometric Back-Propagation in Morphological Neural Networks

Groenendijk, Rick; Dorst, L.; Gevers, T.

doi:10.36227/techrxiv.20330667.v1

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…This approach has shown promise in achieving improved performance and greater flexibility in network design. Also, recent research [25] in this area makes it possible to directly calculate gradients for backpropagation, but so far it has only been carried out for one-layer networks and cannot be used for real tasks.…”

Section: Morphological Networkmentioning

confidence: 99%

Bipolar morphological YOLO network for object detection

Zingerenko,

Limonova

2024

Sixteenth International Conference on Machine Vision (ICMV 2023)

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There are various techniques for decreasing the computational complexity of neural networks, and a number of them use neuron approximations. A bipolar morphological neuron is an approximation of a classical neuron that can be used on FPGAs and ASICs to enhance computational efficiency. It uses 4 distinct computational pathways utilizing addition and maximum functions, in contrast to the traditional neuron which employs multiplication and addition. In this paper, we introduce bipolar morphological YOLO network for object detection task. To train the network, we employ an iterative approach that combines knowledge distillation for backbone and fine-tuning of the network's head. Our experiments, which were conducted using the COCO dataset, yield results that are on par with classical networks. Specifically, the average recall for large images is 0.393 for the BM network and 0.371 for the classical network. Additionally, the average precision values are 0.088 for the BM network and 0.097 for the classical network. These outcomes establish a baseline for object detection using bipolar morphological networks.

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Section: Morphological Networkmentioning

confidence: 99%

Bipolar morphological YOLO network for object detection

Zingerenko,

Limonova

2024

Sixteenth International Conference on Machine Vision (ICMV 2023)

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“…Dimitriades and Maragos investigated the use of purely morphological architectures in computer vision classification and found that these models performed slightly worse than their convolutional counterparts [29]. This has led to an increase in the use of hybrid morphological-convolution network architectures in various domains [28,[30][31][32][33][34]. The sparsity induced by replacing linear operators (such as traditional 2D convolution) with morphological ones has been previously examined in the literature [22,29,35].…”

Section: Related Workmentioning

confidence: 99%

On optimizing morphological neural networks for hyperspectral image classification

Kukushkin,

Bogdan,

Schmid

2024

Sixteenth International Conference on Machine Vision (ICMV 2023)

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Convolutional Neural Networks have become an important tool for various Computer Vision tasks. Yet, increasing complexity of such architectures drives computational costs. To this end, we propose two measures to achieve similar classification results as state-of-the-art architectures while at the same time reducing model complexity significantly. Firstly, we describe a novel type of non-linear parameter-efficient morphological layers inspired by concepts that are well-known and widely used with convolutions. Secondly, we present a set of simple network architectures, organized as optimization framework, which is enhanced by neural architecture search and hyperparameter optimization. In experiments with hyperspectral remote sensing data, we demonstrate that the identified optimal morphological architecture produces results not only comparable with other architectures from the optimization framework, but also comparable or better than selected state-of-the-art neural network architectures for image classification. Depending on the performed task, the proposed optimized architecture requires up to 25 times fewer parameters than actual state-of-the-art networks.

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Machine Learning Clifford Invariants of ADE Coxeter Elements

Chen,

Dechant,

et al. 2024

Adv. Appl. Clifford Algebras

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There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for $$A_8$$ A 8 , $$D_8$$ D 8 and $$E_8$$ E 8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results.

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Geometric Back-Propagation in Morphological Neural Networks

Cited by 3 publications

References 6 publications

Bipolar morphological YOLO network for object detection

Bipolar morphological YOLO network for object detection

On optimizing morphological neural networks for hyperspectral image classification

Machine Learning Clifford Invariants of ADE Coxeter Elements

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